Упражнение 722

Решение:

• $${\largeа)}\ \frac{2{,}56\cdot0{,}44\cdot2{,}25}{3{,}2\cdot0{,}12\cdot0{,}6}=\frac{2{,}56\cdot100\cdot0{,}44\cdot100\cdot2{,}25}{3{,}2\cdot100\cdot0{,}12\cdot100\cdot0{,}6}=\frac{\cancel{256}^{\backslash4}\cdot\cancel{44}^{\backslash11}\cdot2{,}25}{\cancel{320}^{\backslash5}\cdot\cancel{12}^{\backslash3}\cdot0{,}6}=\frac{44\cdot2{,}25}{15\cdot0{,}6}=\frac{44\cdot2{,}25\cdot100}{15\cdot0{,}6\cdot100}=\frac{44\cdot\cancel{225}^{\backslash15}}{\cancel{15}^{\backslash1}\cdot60}=\frac{660}{60}=11$$

• $${\largeб)}\ 5{,}72\cdot\frac{3}{11}=\frac{\cancel{5{,}72}^{\backslash0{,}52}\cdot3}{\cancel{11}^{\backslash1}}=1{,}56$$

• $${\largeв)}\ 8{,}4:2\frac{1}{3}=8{,}4:\frac{7}{3}=8{,}4\cdot\frac{3}{7}=\frac{\cancel{8{,}4}^{\backslash1{,}2}\cdot3}{\cancel7^{\backslash1}}=3{,}6$$

• $${\largeг)}\ 6{,}3\cdot1\frac{2}{9}=6{,}3\cdot\frac{11}{9}=\frac{\cancel{6{,}3}^{\backslash0{,}7}\cdot11}{\cancel9^{\backslash1}}=7{,}7$$

• $${\largeд)}\ 11{,}7:1\frac{6}{7}=11{,}7:\frac{13}{7}=11{,}7\cdot\frac{7}{13}=\frac{\cancel{11{,}7}^{\backslash0{,}9}\cdot7}{\cancel{13}^{\backslash1}}=6{,}3$$

• $${\largeе)}\ \frac{1\frac{2}{7}\cdot2\frac{3}{5}\cdot2\frac{1}{4}}{5\frac{2}{5}\cdot1\frac{6}{7}\cdot\frac{1}{4}}=\frac{\frac{9}{7}\cdot\frac{13}{5}\cdot\frac{9}{4}}{\frac{27}{5}\cdot\frac{13}{7}\cdot\frac{1}{4}}=\frac{9}{7}\cdot\frac{13}{5}\cdot\frac{9}{4}:\frac{27}{5}:\frac{13}{7}:\frac{1}{4}=\frac{9}{7}\cdot\frac{13}{5}\cdot\frac{9}{4}\cdot\frac{5}{27}\cdot\frac{7}{13}\cdot\frac{4}{1}=\frac{\cancel9^{\backslash1}\cdot\cancel{13}^{\backslash1}\cdot9\cdot\cancel5^{\backslash1}\cdot\cancel7^{\backslash1}\cdot\cancel4^{\backslash1}}{\cancel7^{\backslash1}\cdot\cancel5^{\backslash1}\cdot\cancel4^{\backslash1}\cdot\cancel{27}^{\backslash3}\cdot\cancel{13}^{\backslash1}}=\frac{9}{3}=3$$

• $${\largeж)}\ \frac{12\frac{4}{5}\cdot3\frac{3}{4}-4\frac{4}{11}\cdot4\frac{1}{8}}{11\frac{2}{3}:\frac{7}{18}}=\frac{\frac{64}{5}\cdot\frac{15}{4}-\frac{48}{11}\cdot\frac{33}{8}}{\frac{35}{3}\cdot\frac{18}{7}}=\frac{\frac{\cancel{64}^{\backslash16}\cdot\cancel{15}^{\backslash3}}{\cancel5^{\backslash1}\cdot\cancel4^{\backslash1}}-\frac{\cancel{48}^{\backslash6}\cdot\cancel{33}^{\backslash3}}{\cancel{11}^{\backslash1}\cdot\cancel8^{\backslash1}}}{\frac{\cancel{35}^{\backslash5}\cdot\cancel{18}^{\backslash6}}{\cancel3^{\backslash1}\cdot\cancel7^{\backslash1}}}=\frac{48-18}{30}=\frac{30}{30}=1$$

• $${\largeз)}\ \frac{28{,}8:13\frac{5}{7}+6{,}6:\frac{2}{3}}{1\frac{11}{16}:2{,}25}=\frac{28{,}8:\frac{96}{7}+6{,}6:\frac{2}{3}}{\frac{27}{16}:\frac{9}{4}}=\frac{\cancel{28{,}8}^{\backslash0{,}3}\cdot\frac{7\phantom{^{\backslash1}}}{\cancel{96}^{\backslash1}}+\cancel{6{,}6}^{\backslash3{,}3}\cdot\frac{3\phantom{^{\backslash1}}}{\cancel2^{\backslash1}}}{\frac{\cancel{27}^{\backslash3}}{\cancel{16}^{\backslash4}}\cdot\frac{\cancel4^{\backslash1}}{\cancel9^{\backslash1}}}=\frac{2{,}1+9{,}9}{\frac{3}{4}}=12:\frac{3}{4}=12\cdot\frac{4}{3}=\frac{\cancel{12}^{\backslash4}\cdot4}{\cancel3^{\backslash1}}=16$$